The cabinet secretary, Sir Gus O'Donnell, said tonight he was satisfied that the culture secretary, Jeremy Hunt, had not prejudged the BSkyB takeover.

O'Donnell made the statement after John Denham, the shadow business secretary, wrote a letter to him seeking assurances in the wake of business secretary Vince Cable losing all media and telecoms powers to Hunt's department after Cable told undercover reporters he had "declared war" on Rupert Murdoch. Denham cited the requirement that ministers should carry out their duties with objectivity and openness and said Cable's comments raise "serious questions" about the Lib Dem minister's objectivity and his openness during the previous stages of the decision-making process on the proposed News Corp takeover of BSkyB.

The letter sought reassurance that the culture secretary was a "fit and proper person" to arbitrate on News Corp's bid for full control of BSkyB, given his past comments on the subject. It came as Labour leader Ed Miliband branded the coalition government "a sham" and as Nick Clegg was forced to try to scotch the notion that rifts are emerging within ministerial ranks.

O'Donnell said the transfer in responsibility for media competition to the culture secretary was "precisely to ensure there was no conflict of interest" regarding Cable.

He added that prime minister David Cameron had sought his advice about whether there was any legal impediment to the shift in ministerial responsibilities before making a decision yesterday. "I took advice from lawyers and, in providing advice that there was no such impediment I was, of course, aware of the former statements from Mr Hunt which you cite," Sir Gus said.

The Denham letter, sent today, was the latest salvo by Labour as it seized on the contents of the secretly taped comments of Liberal Democrat ministers unhappy with important aspects of government policy to brand the coalition government "a sham".

Leaving his London home earlier today, he insisted that the matter regarding Cable's "very unfortunate" comments had been dealt with. "I think now Vince and the government can move on and that is the end of it," he said.

He added that disagreement was part of the normal business of any government.

"I don't think we should be surprised about the reports of what other ministers have said – that there are differences of opinion in a coalition, as there are indeed in all governments," he said.

"The most important thing is that we get on and work together in the coalition government to fix the mess that we have inherited from Labour. That is what people expect from us and that's exactly what we are doing."

Clegg's efforts to move on from the affair was undermined by further revelations of unease over policies harboured by three ministerial colleagues in fresh revelations contained in secret recordings made by undercover Daily Telegraph reporters.

Michael Moore, the Scottish secretary, said cutting child benefit for higher-rate taxpayers was "blatantly not a consistent and fair thing to do", while the business minister, Ed Davey, said he was "gobsmacked" by the decision. Steve Webb, the pensions minister, revealed he had written to George Osborne seeking changes to the policy because "the details aren't right".

Labour leader Ed Miliband said the Telegraph revelations made clear that "the cracks are starting to widen" in the coalition ranks.

Miliband, who last week described Clegg as the backend of a pantomime horse, with Cameron at the front, told a news conference today: "These are decisions of a Conservative-led government propped up by Liberal Democrat passengers. Passengers not in the front seat, not even in the back seat of the car, but passengers who have got themselves locked in the boot," he said.

Miliband added that he would have sacked Cable if he had been prime minister, and he invited unhappy Lib Dem MPs to join the Labour benches. But David Cameron said he was "content" for Cable to stay in government. "The action I took yesterday was the right action," he told the BBC.

Cameron criticised Miliband for calling the coalition "a sham". He said: "I think he's wrong. This government is delivering in terms of the real problems that the country faces … Just sniping from the sidelines is not constructive. Of course, coalitions have their difficulties and their tensions. But the fact is, we're putting aside personal and political differences to work together in the national interest."

Many had expected an angry David Cameron to sack Cable or transfer him to a lesser cabinet role following his outburst to the undercover reporters.

Tory MP John Whittingdale, the chairman of the Commons culture, media and sport select committee, said Cable would "almost certainly" have been sacked if he were a Conservative minister, but had been kept in post "to keep our partners in the coalition content" .

"Equally, it's quite plain that Vince Cable is the second most important Liberal member of the coalition," he told Radio 4's Today programme.

"We have already lost one leading Liberal minister and the feeling was we cannot afford to lose another."

On the wider unease reflected in the secret tapes, Tim Farron, the Lib Dem president, insisted that, despite points of disagreement, the partnership had proved to be a "much better beast" than the last Labour government, where there was just a semblance of unity.

"We discovered nothing new at all," Farron said of the newspaper revelations.

Moore, the Berwickshire MP, describes the increase in tuition fees to a maximum £9,000 as "the biggest, ugliest, most horrific thing in all of this … a car crash, a train wreck".

Speaking to reporters posing as constituents, Moore said: "I signed a pledge that promised not to do this. I've just done the worst crime a politician can commit, the reason most folk distrust us as a breed. I've had to break a pledge and very, very publicly." He added that Conservative rightwingers "hate us with a passion".

Moore issued a statement later in which he said it should not come as a shock that he was a "committed Liberal Democrat, focused on promoting Liberal Democrat values and policies" . "As I said in my constituency, and many times elsewhere, the coalition has been formed to tackle deep-seated problems in this country and to address the largest-ever deficit in peacetime history.

"That involves tough choices which are not always comfortable to make but the coalition remains committed to ensuring that we tackle the legacy left to us by Labour."